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2 Answers
2

I think the translation "as one would expect" often misses the mark for さすが (even in reference to others). It's close but a little more complicated than that.

Here is Daijisen's definition, with added translations.

1［形動］［文］［ナリ］
１ 評判や期待のとおりの事実を確認し、改めて感心するさま。なるほど、たいしたもの。「この難問が解けるとは さすが だ」
Feeling renewed appreciation for a fact after confirming it matches reputation or expectations.
"You really are skilled to be able to solve a problem this difficult."

2［副］１ あることを認めはするが、特定の条件下では、それと相反する感情を抱くさま。そうは言うものの。それはそうだが、やはり。「味はよいが、これだけ多いと さすがに 飽きる」「非はこちらにあるが、一方的に責められると さすがに 腹が立つ」
Holding feelings of acceptance towards something, but opposition to it under specific conditions.
"The taste is good, but when there's this much of it I just am going to tire of it"
"I'm at fault, but being blamed over and over is going to anger you regardless"

３ （「さすがの…も」の形で）そのものの価値を認めはするが、特定の条件下では、それを否定するさま。さしもの。「さすが の名探偵も今度ばかりはお手上げだろう」
(In the form "さすがの…も") Accepting the merit of something, but rejecting it under specific conditions.
"Even the (meritous) famous detectives would throw their hands up at this one."

Your example falls under either 2.1 or 2.2 depending on the context.

If someone asked you to do something, and you replied with a sigh さすがに眠い, the meaning is "I'd normally be in favor, but because I am (too) tired, I'm opposed" (2.1).

If you were saying this line to yourself seemingly at random, it would be you internally admitting / acknowledging the fact that you're tired (2.2).

"As one would expect" doesn't have to be a compliment. In the example you've provided, the meaning is "as one would expect I'm sleepy", with the reason for being sleepy implied to be known to the listener/reader. For instance, not having slept last night because you were finishing a report.